Re: evaluating functions and displaying results numerically

• To: mathgroup at smc.vnet.net
• Subject: [mg126211] Re: evaluating functions and displaying results numerically
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Wed, 25 Apr 2012 00:35:12 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Problems I can see off-hand, in order:

1) You didn't post your code, since Ref is undefined.

2) You didn't post much of your output, either... though enough to see
some problems.

3) Mathematica absolutely WILL NOT return a symbolic answer if even ONE of
the terms is Real and the others have a numeric value. For instance:

1. + Sin[1] + Pi

4.98306

The first term is Real and the other two are numeric, so the sum is Real.

4) The output in your PDF shows at least three unevaluated If statements.
That only happens if the first argument of If is undetermined by your
input. Show me the Ref function, and I might be able to explain how that
occurred in your case, but it's definitely not Mathematica's fault.

5) Abs will return a symbolic answer if its argument is symbolic, which it
certainly WILL be if there are unevaluated If statements in it.

6) The output also shows the following term inside the first call to Abs
(I think; it's a bit hard to read):

161.100 I | 1.[<<5>>,<<2>>]

That means you have a syntax error that tried to use 161.100 I | 1. as a
function name.

| is the symbol for Alternatives, so it should only appear in patterns.

Post the code, and I'm sure you'll get better answers.

Bobby

On Tue, 24 Apr 2012 14:30:42 -0500, Eduardo Fontana
<prof.eduardofontana at gmail.com> wrote:

> I already had used the options you suggested. In fact if you look at the
> arguments of the function I defined, which are decimaln arguments, there
> is no reason for Mathematica to output 1000 terms instead of calculating
> the sum. I havent yet found a satisfactory explanation for what
> happened. I changed calculated the summation using a for loop and
> numerical results are now being obtained. But still I have no idea as
> for the reason my original code didnt yield numerical results (yes, I
> used the N option as well)
> regards
> Eduardo Fontana, PhD
> Professor Titular
> Dep. de Eletr=F4nica e Sistemas
> UFPE - Centro de Tecnologia e Geoci=EAncias
> Bloco A, Sala 421 Recife - PE 50.740-550
> Skype: edu.fontana
> Phones: +5581-21267792, +5511-30424021
> http://www.ufpe.br/fontana
>
> On Apr 24, 2012, at 12:08 PM, DrMajorBob wrote:
>
>> Symbol in, symbol out... to keep things just as EXACT as you entered
>> them.
>>
>> If Mathematica cannot identify simplifications and cancellations, the
>> sum of 1000 terms is returned exactly, because you gave exact inputs.
>> Use decimal inputs, N, or SetPrecision to get approximations.
>>
>> Bobby
>>
>> On Tue, 24 Apr 2012 04:30:08 -0500, Eduardo Fontana
>> <prof.eduardofontana at gmail.com> wrote:
>>
>>>
>>>> My reply to Kevin is now being sent to others who kindly replied to
>>> this topic. I attached a image file but it was returned by the
>>> moderator.
>>>
>>> might help. The output file is in a pdf document on google docs on the
>>> regards to all
>>> Eduardo
>>>
>>> Dear Kevin
>>>
>>> though I havent had this interpretation of results from Mathematica
>>> before. I never had to use the N option befor. What about my second
>>> enquire, reproduced below
>>>>>> In another instance, I have a summation of about 1000 terms defined
>>>>>> as
>>>>>> a function of 3 arguments. When I use numerical arguments to
>>>>>> calculate the summation, instead of
>>>>>> Mathematica calculating a numerical result it generates a symbolic
>>>>>> output with all 1000 terms.
>>>> It doesnt make sense that Mathematica chooses to do the whole thing
>>>> symbolically. I have made similar calculations before, and
>>>> Mathematica performed the calculation numerically. I presume that I
>>>> have enabled some sort of symbolic calculation, but I cannot find
>>>> where. I am attaching a a link to a pdf file showing a image of the
>>>> generated result for my function called "Absorption". The other
>>>> functions are defined prior to the definition of Absorption. I just
>>>> want to show the type of result generated. Also, If I want to plot my
>>>> function Absorption relative to one of the arguments, Mathematica
>>>> just doesnt plot it.
>>>> Best regards
>>> The output image is in the google docs file below
>>> Eduardo Fontana, PhD
>>> Professor Titular
>>> Dep. de Eletr==F4nica e Sistemas
>>> UFPE - Centro de Tecnologia e Geoci==EAncias
>>> Bloco A, Sala 421 Recife - PE 50.740-550
>>> Skype: edu.fontana
>>> Phones: +5581-21267792, +5511-30424021
>>> http://www.ufpe.br/fontana
>>>
>>>>
>>>> 2012/4/21 Kevin J. McCann <kjm at kevinmccann.com>:
>>>>> The output Sin[1] is what is called an "exact", i.e. you gave
>>>>> Mathematica an exact
>>>>> input 1, not 1.0; so, Mathematica returned an exact. If you want a
>>>>> function ==
>>> to give
>>>>> a numerical, i.e. machine precision output, do something like this:
>>>>>
>>>>> Sin[1]//N
>>>>>
>>>>> or
>>>>>
>>>>> N[Sin[1]]
>>>>>
>>>>> That is, wrap the result in N[], the number function.
>>>>>
>>>>> Cheers,
>>>>>
>>>>> Kevin
>>>>>
>>>>> On 4/21/2012 12:35 AM, Eduardo Fontana wrote:
>>>>>>
>>>>>> Once in a while a face a problem with Mathematica in which I cannot
>>>>>> get a straightforward numerical output.
>>>>>> I have a function defined in mathematica, I try to evaluate the
>>>>>> function with numerical arguments and mathematica returns a replica
>>>>>> of
>>>>>> my function with the same arguments. It must be something I set
>>>>>> without noticing. I cannot get numerical results at all.
>>>>>> In another instance, I have a summation of about 1000 terms defined
>>>>>> as
>>>>>> a function of 3 arguments. When I use numerical arguments, instead
>>>>>> of
>>>>>> Mathematica calculating a numerical result it generates a symbolic
>>>>>> output with all 1000 terms. Even if a try something very simple such
>>>>>> as
>>>>>> In[1]: Sin[1]
>>>>>> the output is
>>>>>> Out[1]: Sin[1]
>>>>>> Could anyone give me a clue on this?
>>>>>> regards
>>>>>>
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> Eduardo Fontana, PhD
>>>> Professor Titular
>>>> Dep. de Eletr==F4nica e Sistemas
>>>> UFPE - Centro de Tecnologia e Geoc==EAncias, Bloco A, Sala 421
>>>> Recife - Pernambuco - 50.740-550
>>>> Fone (Phone): +5581-21267792
>>>> Skype Phone: +5511-30424021
>>>> Skype: edu.fontana
>>>>
>>>> On Apr 21, 2012, at 8:16 AM, Kevin J. McCann wrote:
>>>>
>>>>> The output Sin[1] is what is called an "exact", i.e. you gave
>>>>> Mathematica an exact input 1, not 1.0; so, Mathematica returned an
>>>>> exact. If you want a function to give a numerical, i.e. machine
>>>>> precision output, do something like this:
>>>>>
>>>>> Sin[1]//N
>>>>>
>>>>> or
>>>>>
>>>>> N[Sin[1]]
>>>>>
>>>>> That is, wrap the result in N[], the number function.
>>>>>
>>>>> Cheers,
>>>>>
>>>>> Kevin
>>>>>
>>>>> On 4/21/2012 12:35 AM, Eduardo Fontana wrote:
>>>>>> Once in a while a face a problem with Mathematica in which I cannot
>>>>>> get a straightforward numerical output.
>>>>>> I have a function defined in mathematica, I try to evaluate the
>>>>>> function with numerical arguments and mathematica returns a replica
>>>>>> of
>>>>>> my function with the same arguments. It must be something I set
>>>>>> without noticing. I cannot get numerical results at all.
>>>>>> In another instance, I have a summation of about 1000 terms defined
>>>>>> as
>>>>>> a function of 3 arguments. When I use numerical arguments, instead
>>>>>> of
>>>>>> Mathematica calculating a numerical result it generates a symbolic
>>>>>> output with all 1000 terms. Even if a try something very simple such
>>>>>> as
>>>>>> In[1]: Sin[1]
>>>>>> the output is
>>>>>> Out[1]: Sin[1]
>>>>>> Could anyone give me a clue on this?
>>>>>> regards
>>>>>>
>>>>
>>>> Eduardo Fontana, PhD
>>>> Professor Titular
>>>> Dep. de Eletr==F4nica e Sistemas
>>>> UFPE - Centro de Tecnologia e Geoci==EAncias
>>>> Bloco A, Sala 421, Recife - PE 50740-550
>>>>
>>>>
>>>>
>>
>>
>> --
>> DrMajorBob at yahoo.com
>

--
DrMajorBob at yahoo.com

```

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